Related papers: A note on algebraic potentials and Morales-Ramis t…

Almost any reasonable class of finite relational structures has the Ramsey property or a precompact Ramsey expansion. In contrast to that, the list of classes of finite algebras with the precompact Ramsey expansion is surprisingly short. In…

We introduce the notion of "quasi-symmetric" polynomials, which is a generalization of the notion of symmetry, and is particularly suited to the setting of polynomial rings over finite fields. The properties of this new class of functions…

We prove an integrability criterion and a partial integrability criterion for homogeneous potentials of degree -1 which are invariant by rotation. We then apply it to the proof of the meromorphic non-integrability of the n body problem with…

In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and…

Recently continuous rational maps between real algebraic varieties have attracted the attention of several researchers. In this paper we continue the investigation of approximation properties of continuous rational maps with values in…

Probabilistic argumentation is an alternative to causal modeling with Bayesian networks. Probabilistic argumentation structures (PAS) are defined on families of compatible frames (f.c.f). This is a generalization of the usual multivariate…

After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…

Consider the semialgebraic structure over the real field. More generally, let an ominimal structure be over a real closed field. We show that a definable metric space X with a definable metric d is embedded into a Euclidean space so that…

We state criteria for a nilpotent Lie algebra $\g$ to admit an invariant metric. We use that $\g$ possesses two canonical abelian ideals $\ide(\g) \subset \mathfrak{J}(\g)$ to decompose the underlying vector space of $\g$ and then we state…

Some of the strategies which have been put forward in order to deal with the inconsistency between quantum mechanics and special relativity are examined. The EPR correlations are discussed as a simple example of quantum mechanical…

Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…

In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…

We study the influence of an additional scalar potential on various geometric and analytic properties of Dirac-harmonic maps. We will create a mathematical wish list of the possible benefits from inducing the potential term and point out…

We investigate an analogue of the Wedderburn principal theorem for associative conformal algebras with finite faithful representations. It is shown that the radical splitting property for an algebra of this kind holds if the maximal…

A cubic algebraic equation for the effective parametrizations of the standard gravitational Lagrangian has been obtained without applying any variational principle.It was suggested that such an equation may find application in gravity…

The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…

The Colombeau algebra of generalized functions allows to unrestrictedly carry out products of distributions. We analyze this operation from a microlocal point of view, deriving a general inclusion relation for wave front sets of products in…

The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…

In this paper, we study arithmetic dynamics in arbitrary characteristic, in particular in positive characteristic. We generalise some basic facts on arithmetic degree and canonical height in positive characteristic. As applications, we…

This paper aims to introduce the concept of nilpotency and capability in multiplicative Lie algebras. Also, we see the existence of covers of a multiplicative Lie algebra and thoroughly examine their relationships with capable and perfect…